Algebraic may refer to any subject related to algebra in mathematics and related branches like

algebraic number theory Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic ob ...

and algebraic topology. The word algebra itself has several meanings. Algebraic may also refer to: * Algebraic data type, a datatype in computer programming each of whose values is data from other datatypes wrapped in one of the constructors of the datatype *

Algebraic number An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, (1 + \sqrt)/2, is an algebraic number, because it is a root of the po ...

s, a complex number that is a root of a non-zero polynomial in one variable with integer coefficients * Algebraic functions, functions satisfying certain polynomials *

Algebraic element In mathematics, if is a field extension of , then an element of is called an algebraic element over , or just algebraic over , if there exists some non-zero polynomial with coefficients in such that . Elements of which are not algebraic o ...

, an element of a field extension which is a root of some polynomial over the base field * Algebraic extension, a field extension such that every element is an algebraic element over the base field *

Algebraic definition In mathematical logic, an algebraic definition is one that can be given using only equations between terms with free variables. Inequalities and quantifiers are specifically disallowed. Saying that a definition is algebraic is a stronger condition ...

, a definition in mathematical logic which is given using only equalities between terms *

Algebraic structure In mathematics, an algebraic structure consists of a nonempty set ''A'' (called the underlying set, carrier set or domain), a collection of operations on ''A'' (typically binary operations such as addition and multiplication), and a finite set of ...

, a set with one or more finitary operations defined on it * Algebraic, the order of entering operations when using a calculator (contrast reverse Polish notation) *

Algebraic sum In mathematics, summation is the addition of a sequence of any kind of numbers, called ''addends'' or ''summands''; the result is their ''sum'' or ''total''. Beside numbers, other types of values can be summed as well: functions, vectors, matr ...

, a summation of quantities that takes into account their signs; e.g. the algebraic sum of 4, 3, and -8 is -1.

See also